Finite Group Databasebeta

← #20255007

Subgroups — #20255007

Order 6016.

556 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094048C212yesmaximal, complemented
2#15689793C211yesmaximal, characteristic, complemented
3#15689758C211yesmaximal, characteristic, complemented
4#15689373C212yesmaximal, complemented
5#15689320C211yesmaximal, characteristic, complemented
6#15689315C211yesmaximal, characteristic, complemented
7#15689265C212yesmaximal, complemented
8#15689255C212yesmaximal, complemented
9C4×#10625325C211yesmaximal, characteristic, complemented
10#15689202C211yesmaximal, characteristic, complemented
11C47×#493C211yesmaximal, characteristic, complemented
12C2×#10625352C2212yescomplemented
13C2×D4×D47—21no—
14C2×D4×D47C2212yes—
15#13094048—28no—
16C2×#10625325C2211yescharacteristic
17C2×#10625335C2212yescomplemented
18C2×#10625334C2212yes—
19C2×#10625324C2212yescomplemented
20#13094020—21no—
21#13093996—22no—
22#13093995—21no—
23#13093995C2212yes—
24#13093995C2212yescomplemented
25#13093992—22no—
26C4×Dic94C2211yescharacteristic, complemented
27C4×D188C2211yescharacteristic
28C4×D188C2211yescharacteristic
29D4×Dic47—21no—
30#13093956C2211yescharacteristic, complemented
31C4⋊(C47⋊C8)C2211yescharacteristic, complemented
32#13093949C2211yescharacteristic, complemented
33#13093946C2211yescharacteristic
34#13093945C2212yescomplemented
35#13093945C2212yescomplemented
36(C2×D47)⋊C8C2212yescomplemented
37C2×D8×C47C2212yescomplemented
38C2×D8×C47C2212yescomplemented
39#127×C47C2211yescharacteristic
40#127×C47C2211yescharacteristic, complemented
41C4×C8×C47C2211yescharacteristic, complemented
42C23×D47—22no—
43C2×D4×C47—21no—
44C2×D4×C47—21no—
45C2×D4×C47—21no—
46C2×D4×C47—21no—
47C2×D4×C47C2312yes—
48C2×D4×C47C2312yes—
49C2×C22⋊D47—22no—
50C2×C22⋊D47—22no—
51C2×C22⋊D47—22no—
52C2×C22⋊D47—22no—
53C22×Dic47—22no—
54#10625352—24no—
55#10625352—42no—
56D4×D47—24no—
57D4×D47—42no—
58D4×D47—44no—
59C2×D188D411yescharacteristic
60C2×D188C2311yescharacteristic
61C2×C4×D47—21no—
62C2×C4×D47C2312yes—
63C2×Dic94C2311yescharacteristic
64D8×C47—24no—
65D8×C47—42no—
66C2×C8×C47C2311yescharacteristic
67C2×C8×C47C2311yescharacteristic
68C42×C47C2311yescharacteristic
69C22⋊Dic47—22no—
70C22⋊Dic47—22no—
71#10625335—24no—
72#10625334—24no—
73(C2×D47)⋊C4—21no—
74(C2×D47)⋊C4D412yes—
75C4⋊Dic47D411yescharacteristic
76C4⋊Dic47C2311yescharacteristic
77C4⋊Dic47C2311yescharacteristic
78Dic47⋊C4—21no—
79C4×Dic47—21no—
80C2×C47⋊C8C2312yes—
81#10625325D414yescomplemented
82#10625324—24no—
83C23×C47—22no—
84C23×C47—22no—
85C22×D47—21no—
86C22×D47—44no—
87C22×D47—44no—
88C22×D47—82no—
89C22×D47C2×D412yes—
90D4×C47—22no—
91D4×C47—22no—
92D4×C47—22no—
93D4×C47—22no—
94D4×C47—42no—
95D4×C47—42no—
96D4×C47—81no—
97D4×C47—81no—
98C2×C4×C47C2×D411yescharacteristic
99C2×C4×C47C2×D411yescharacteristic
100C2×C4×C47C2411yescharacteristic
101C22⋊D47—44no—
102C22⋊D47—44no—
103C22⋊D47—44no—
104C22⋊D47—82no—
105C2×Dic47—21no—
106C2×Dic47—21no—
107C2×Dic47—21no—
108C2×Dic47—44no—
109C2×Dic47C2×D412yes—
110D188—22no—
111D188—21no—
112D188C2×D412yes—
113C4×D47—22no—
114C4×D47—22no—
115C4×D47—42no—
116Dic94—21no—
117Dic94C2×D412yescomplemented
118C8×C47—21no—
119C8×C47C2×D412yescomplemented
120C47⋊C8—22no—
121C22×C47—42no—
122C22×C47—42no—
123C22×C47—42no—
124C22×C47—42no—
125C22×C47—42no—
126C22×C47—42no—
127C22×C47C22×D411yescharacteristic
128C2×D47—22no—
129C2×D47—22no—
130C2×D47—22no—
131C2×D47—22no—
132C2×D47—41no—
133C2×D47—41no—
134C2×D47—88no—
135C4×C47—21no—
136C4×C47AGL(1,ℤ/8)12yescomplemented
137C4×C47C22×D411yescharacteristic
138C4×C47H(5,𝔽2)11yescharacteristic
139Dic47—22no—
140Dic47—22no—
141Dic47—41no—
142Dic47—41no—
143#3274—471nomaximal, Sylow
144C2×C47—82no—
145C2×C47—82no—
146C2×C47D4211yescharacteristic
147C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
148C2×C47#57611yescharacteristic
149D47—42no—
150D47—42no—
151C2×AGL(1,ℤ/8)—472no—
152#550—471no—
153D42—471no—
154#493D4711yescharacteristic, complemented
155#469—472no—
156#460—471no—
157#459—471no—
158#449—472no—
159#447—472no—
160C4×SD16—471no—
161#436—471no—
162C47#327411yescharacteristic, complemented, Sylow
163C2×#41—472no—
164C22×D4—472no—
165C22×D4—941no—
166AGL(1,ℤ/8)—948no—
167C2×SD16—472no—
168C2×SD16—471no—
169C2×D8—472no—
170C2×D8C2×D4712yescomplemented
171C2×D8C2×D4712yescomplemented
172C2×M16—472no—
173#127—941no—
174#127C2×D4711yescharacteristic
175#127C2×D4711yescharacteristic, complemented
176#121—472no—
177#121—472no—
178#121—942no—
179#121—941no—
180#120—942no—
181C4×Q8—471no—
182C4×D4—471no—
183C4×D4—471no—
184C4×D4—941no—
185#106—471no—
186C4⋊C8—471no—
187#103—471no—
188#102—472no—
189#102—472no—
190#102—471no—
191C22⋊C8—472no—
192C4×C8C2×D4711yescharacteristic, complemented
193C24—942no—
194#41—944no—
195#41—1882no—
196C2×Q8—471no—
197C2×D4—21no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—21no—
201C2×D4—471no—
202C2×D4—471no—
203C2×D4—942no—
204C2×D4—944no—
205C2×D4—942no—
206C2×D4—942no—
207C2×D4—942no—
208C2×D4—1882no—
209C2×D4—1884no—
210C2×D4C22×D4712yes—
211C2×D4C22×D4712yes—
212C22×C4—472no—
213C22×C4—942no—
214C22×C4—941no—
215SD16—474no—
216SD16—944no—
217D8—24no—
218D8—42no—
219D8—944no—
220M16—944no—
221C2×C8—472no—
222C2×C8C22×D4711yescharacteristic
223C2×C8C22×D4711yescharacteristic
224C4⋊C4—471no—
225C4⋊C4—471no—
226C4⋊C4—471no—
227C4⋊C4—941no—
228C22⋊C4—472no—
229C22⋊C4—942no—
230C22⋊C4—942no—
231C22⋊C4—941no—
232C42—941no—
233C42C22×D4711yescharacteristic
234C23—22no—
235C23—22no—
236C23—472no—
237C23—941no—
238C23—3762no—
239C23—1884no—
240C23—1884no—
241Q8—472no—
242Q8—941no—
243D4—22no—
244D4—22no—
245D4—22no—
246D4—22no—
247D4—42no—
248D4—42no—
249D4—81no—
250D4—81no—
251D4—472no—
252D4—942no—
253D4—941no—
254D4—3762no—
255D4—1884no—
256D4—1884no—
257D4—1884no—
258C2×C4—472no—
259C2×C4—941no—
260C2×C4—942no—
261C2×C4—942no—
262C2×C4—941no—
263C2×C4—941no—
264C2×C4—1884no—
265C2×C4—1882no—
266C2×C4D4×D4711yescharacteristic
267C2×C4D4×D4711yescharacteristic
268C2×C4C23×D4711yescharacteristic
269C8—21no—
270C8—942no—
271C8D4×D4712yescomplemented
272C22—42no—
273C22—42no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—942no—
279C22—942no—
280C22—942no—
281C22—942no—
282C22—3768no—
283C22—1881no—
284C22—1881no—
285C22C2×D4×D4711yescharacteristic
286C4—21no—
287C4—942no—
288C4—942no—
289C4—1881no—
290C4—1881no—
291C4#1309404812yescomplemented
292C4C2×D4×D4711yescharacteristic
293C4#1309406911yescharacteristic
294C2—82no—
295C2—82no—
296C2—1882no—
297C2—1882no—
298C2#1568975811yescharacteristic
299C2C2×#1309404811yescharacteristic
300C2#1568992411yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#493C2
socleC22×C47C22×D4
hypercenter#493D47
hypocenterC47#3274
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#13094048C2semidirect
2. #15689793C2semidirect
3. #15689758C2semidirect
4. #15689373C2semidirect
5. #15689320C2semidirect
6. #15689315C2semidirect
7. #15689265C2semidirect
8. #15689255C2semidirect
9. C4×#10625325C2semidirect
10. #15689202C2semidirect
11. C47×#493C2semidirect
12. C2×#10625352C22semidirect
17. C2×#10625335C22semidirect
19. C2×#10625324C22semidirect
24. #13093995C22semidirect
26. C4×Dic94C22semidirect
30. #13093956C22semidirect
31. C4⋊(C47⋊C8)C22semidirect
32. #13093949C22semidirect
34. #13093945C22semidirect
35. #13093945C22semidirect
36. (C2×D47)⋊C8C22semidirect
37. C2×D8×C47C22semidirect
38. C2×D8×C47C22semidirect
40. #127×C47C22semidirect
41. C4×C8×C47C22semidirect
81. #10625325D4semidirect
117. Dic94C2×D4semidirect
119. C8×C47C2×D4semidirect
136. C4×C47AGL(1,ℤ/8)semidirect
154. #493D47semidirect
162. C47#3274semidirect
170. C2×D8C2×D47semidirect
171. C2×D8C2×D47semidirect
175. #127C2×D47semidirect
192. C4×C8C2×D47semidirect
271. C8D4×D47semidirect
291. C4#13094048semidirect